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college mathematics for business

Questions and Answers of College Mathematics For Business

An investment of $10,000 earns interest at an annual rate of 7.5% compounded continuously.(A) Find the instantaneous rate of change of the amount in the account after 1 year.(B) Find the
The number x of compact refrigerators that people are willing to buy per week from an appliance chain at a price of $p is given byUse implicit differentiation to find dp/dx. x = 900 – 30Vp + 25
The number x of fitness watches that people are willing to buy per week from an online retailer at a price of $p is given byx = 5,000 - 0.1p2Use implicit differentiation to find dp/dx.
In Problem(A) Find f′(x) using the quotient rule,(B) Explain how f′(x) can be found easily without using the quotient rule. 1 f(x)
In Problem use the price–demand equation p + 0.004x = 32, 0 ≤ p ≤ 32.If p = $13 and the price is decreased, will revenue increase or decrease?
The number x of compact refrigerators that an appliance chain is willing to sell per week at a price of $p is given byUse implicit differentiation to find dp/dx. x = 60Vp + 50 – 300
In Problem find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x.f(x) = x(4 - x)3; x = 2
In Problem(A) Find f′(x) using the quotient rule,(B) Explain how f′(x) can be found easily without using the quotient rule. -1 f(x) = %3D
In Problem use the price–demand equation p + 0.004x = 32, 0 ≤ p ≤ 32.If p = $21 and the price is decreased, will revenue increase or decrease?
In Problem(A) Find f′(x) using the quotient rule,(B) Explain how f′(x) can be found easily without using the quotient rule. -3 f(x) %3D 4 x*
In Problem find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x. f(x) x = 3 (2r – 5)3"
In Problem find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x.f(x) = x2(1 - x)4; x = 2
In Problem(A) Find f′(x) using the quotient rule,(B) Explain how f′(x) can be found easily without using the quotient rule. f(x) %3D
In Problem find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x. x4 f(x) x = 4 (Зх — 8)2"
In Problem use graphical approximation methods to find the points of intersection of f(x) and g(x) (to two decimal places).f(x) = ex; g(x) = x5
In Problem find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = VIn x; x = e
In Problem use graphical approximation methods to find the points of intersection of f(x) and g(x) (to two decimal places).f(x) = (ln x)2 ; g(x) = x
The speed of sound in air is given by the formulav = k√Twhere v is the velocity of sound, T is the temperature of the air, and k is a constant. Use implicit differentiation to find dT/dv.
In Problem find f′(x) and find the equation of the line tangent to the graph of f at x = 2.f(x) = (1 + 3x) (5 - 2x)
The equationis Newton’s law of universal gravitation. G is a constant and F is the gravitational force between two objects having masses m1 and m2 that are a distance r from each other. Use
In Problem find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = eV. x = 1 %3D
In Problem use graphical approximation methods to find the points of intersection of f(x) and g(x) (to two decimal places).f(x) = (ln x)3 ; g(x) = x
In Problem find f′(x) and find the equation of the line tangent to the graph of f at x = 2. х — 8 f(x) Зх — 4
In Problem find f′(x) and find the equation of the line tangent to the graph of f at x = 2.f(x) = (7 - 3x) (1 + 2x)
In Problem use graphical approximation methods to find the points of intersection of f(x) and g(x) (to two decimal places).f(x) = ln x; g(x) = x1/5
In Problem find f′(x) and find the equation of the line tangent to the graph of f at x = 2. f(x) 2*
In Problem find f′(x) and find the value(s) of x where the tangent line is horizontal.f(x) = x2(x - 5)3
In Problem find f′(x) and find the value(s) of x where the tangent line is horizontal. f(x) = Vx? – 8x + 20
In Problem find f′(x) and find the value(s) of x where the tangent line is horizontal. X - 1 f(x) || (x - 3)3
In Problem use graphical approximation methods to find the points of intersection of f(x) and g(x) (to two decimal places).f(x) = ln x; g(x) = x1/4
In Problem find f′(x) and find the value(s) of x where the tangent line is horizontal.f(x) = x3(x - 7)4
In Problem find f′(x) and find the value(s) of x where the tangent line is horizontal. f(x) = Vx? + 4x + 5
A student reasons that the functions f(x) = ln[5(x2 + 3)4] and g(x) = 4 ln(x2 + 3) must have the same derivative since he has entered f(x), g(x), f′(x), and g′(x) into a graphing calculator, but
In Problem find f′(x) and find the value(s) of x where f′(x) = 0. f(x) x + 1
In Problem find f′(x) and find the value(s) of x where f′(x) = 0. f(x) .2 x + 9
In Problem find f′(x) and find the value(s) of x where f′(x) = 0.f(x) = (2x - 15) (x2 + 18)
A student reasons that the functions f(x) = (x + 1)ln (x + 1) - x and g(x) = (x + 1)1/3 must have the same derivative since she has entered f(x), g(x), f ′(x), and g′(x) into a graphing
In Problem find f′(x) and find the value(s) of x where f′(x) = 0.f(x) = (2x - 3) (x2 - 6)
A single cholera bacterium divides every 0.5 hour to produce two complete cholera bacteria. If we start with a colony of 5,000 bacteria, then after t hours, there will beA(t) = 5,000 . 22t = 5,000 .
In psychology, the Weber– Fechner law for the response to a stimulus iswhere R is the response, S is the stimulus, and S0 is the lowest level of stimulus that can be detected. Find dR/dS. S R = k
In Problem find f′(x) in two ways: (1) Using the product or quotient rule(2) Simplifying first. x* + 4 f(x)
If a price–demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given byIn
An experiment was set up to find a relationship between weight and systolic blood pressure in children. Using hospital records for 5,000 children, the experimenters found that the systolic blood
In Problem find f′(x) in two ways: (1) Using the product or quotient rule(2) Simplifying first. х +9 f(x) %3D
In Problem find f′(x) in two ways: (1) Using the product or quotient rule(2) Simplifying first.f(x) = x3 (x4 - 1)
In Problem give the domain of f, the domain of g, and the domain of m, where m(x) = f [g(x)].f(u) = ln u; g(x) = √x
In Problem find f′(x) in two ways: (1) Using the product or quotient rule(2) Simplifying first.f(x) = x4 (x3 - 1)
In Problem give the domain of f, the domain of g, and the domain of m, where m(x) = f [g(x)].f(u) = eu; g(x) = √x
If a price–demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given byIn
In Problem find each indicated derivative and simplify. f'(w) for f(w) = (w + 1)2"
In Problem give the domain of f, the domain of g, and the domain of m, where m(x) = f [g(x)]. f(u) g(x) =
In Problem find each indicated derivative and simplify. 8'(w) for g(w) = (w - 5) log3 w
In Problem give the domain of f, the domain of g, and the domain of m, where m(x) = f [g(x)].f(u) = √u; g(x) = ex
In Problem find each indicated derivative and simplify. dy for y = 9x'/3 (x³ + 5) dx
In Problem give the domain of f, the domain of g, and the domain of m, where m(x) = f [g(x)]. 1 f(u) u? - g(x) = In x
In Problem find each derivative and simplify. d [3x(x²+ 1)'] dx
In Problem give the domain of f, the domain of g, and the domain of m, where m(x) = f [g(x)].f(u) = ln u; g(x) = 4 - x2
An investment of $25,000 earns interest at an annual rate of 8.4% compounded continuously.(A) Find the instantaneous rate of change of the amount in the account after 2 years.(B) Find the
In Problem find each indicated derivative and simplify. log2 x y' for y = 1 + x?
In Problem find each derivative and simplify. d (x – 7)4 dx 2x3
In Problem find each indicated derivative and simplify. 63 Vĩ f'(x) for f(x) x? – 3
In Problem give the domain of f, the domain of g, and the domain of m, where m(x) = f [g(x)].f(u) = ln u; g(x) = 2x + 10
In Problem find each derivative and simplify. d -log2(3x2- dx 1)
In Problem find each indicated derivative and simplify. 0.2t 8'(1) if g(t) 312 - 1 ||
In Problem find each derivative and simplify. d log (x - 1) dx -
In Problem find each derivative and simplify. d -10+x dx
In Problem find each indicated derivative and simplify. d [4x log x'] dx
In Problem find each derivative and simplify. d 81- dx 1-2r2 272
A fast-food restaurant can produce a hamburger for $2.50. If the restaurant’s daily sales are increasing at the rate of 30 hamburgers per day, how fast is its daily cost for hamburgers increasing?
In Problem find each derivative and simplify. d log3 (4x + 5x + 7) dx
In Problem find each indicated derivative and simplify. dy for y = (x - 1) (x + x + 1) dx
The price–demand equation for hamburgers at a fast-food restaurant isx + 400p = 3,000Currently, the price of a hamburger is $3.00. If the price is increased by 10%, will revenue increase or
In Problem find each derivative and simplify. 2-+4x+ dx 1
The price–demand equation for an order of fries at a fast-food restaurant isx + 1,000p = 2,500Currently, the price of an order of fries is $0.99. If the price is decreased by 10%, will revenue
In Problem find each indicated derivative and simplify.f′(x) for f(x) = (x4 + x2 + 1) (x2 - 1)
Refer to Problem 85. What price will maximize the revenue from selling hamburgers?Problem 85Currently, the price of a hamburger is $3.00. If the price is increased by 10%, will revenue increase or
In Problem find each derivative and simplify. d -10hx dx
In Problem find each indicated derivative and simplify.y′ for y = (x2 + x + 1) (x2 - x + 1)
In Problem find each indicated derivative and simplify.g′(t) for g(t) = (t + 1) (t4 - t3 + t2 - t + 1)
The total cost (in hundreds of dollars) of producing x cell phones per day is(see the figure).(A) Find C′(x).(B) Find C′(24) and C′(42). Interpret the results. C(x) 10 + V2x + 16 0
In Problem find each indicated derivative and simplify. t In t dy for y = dt et
In Problem find each indicated derivative and simplify. dy for du y = 1 + In u
A model for the number of robberies per 1,000 population in the United States (Table 4) isr(t) = 3.2 - 0.7 ln twhere t is years since 1990. Find the relative rate of change for robberies in 2025.
The total sales S (in thousands) of a video game are given bywhere t is the number of months since the release of the game.(A) Find S′(t).(B) Find S(10) and S′(10). Write a brief interpretation
A model for the number of aggravated assaults per 1,000 population in the United States (Table 4) isa(t) = 5.9 - 1.1 ln twhere t is years since 1990. Find the relative rate of change for assaults in
In Problem find f′(x) and simplify. et f(x) x + 1
In Problem find f′(x) and simplify. x - 4 f(x) x? + 5 .2
A point is moving on the graph of y = ex + x + 1 in such a way that its x coordinate is always increasing at a rate of 3 per second. How fast is the y coordinate changing when the point crosses the x
Water is leaking onto a floor. The resulting circular pool has an area that is increasing at the rate of 24 square inches per minute. How fast is the radius R of the pool increasing when the radius
A 17-foot ladder is placed against a wall. If the foot of the ladder is pushed toward the wall at 0.5 foot per second, how fast is the top of the ladder rising when the foot is 8 feet from the wall?
In Problem find f′ (x).f(x) = eex
In Problem find f′(x) and simplify. * + 2 x2 - 3 f(x)
In Problem find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.f(x) = 5,100 - 3x2; x = 35
In Problem find f′(x) and simplify.f(x) = (x4 + 1)-2
A note will pay $20,000 at maturity 10 years from now. How much should you be willing to pay for the note now if money is worth 5.2% compounded continuously?
A point is moving on the graph of y2 - 4x2 = 12 so that its x coordinate is decreasing by 2 units per second when (x, y) = (1, 4). Find the rate of change of the y coordinate.
In Problem find the logarithmic derivatives.f(x) = 1 + x2
In Problem find f′ (x).f(x) = ex + xe
In Problem find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.f(x) = 225 + 65x; x = 15
In Problem find f′(x) and simplify.f(x) = (2x - 5)1/2

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